I understand that dragoons typically fought on foot, using the horse really just to get around quickly, but in the in between action periods how did they carry the musket around? I see saddle holster often with muzzle pointing down, but if the needs of warfare demanded a shot be ready at a moment's notice how would the ball stay in the barrel especially with gravity and jostling of the horse? Even in attack their primary advantage seems like it would be lost if after dismounting they have to load before engaging.
A secondary question pertains to gear in general. I imagine the equipment needed for a dragoon would be pretty different from that of foot or light infantry. What sort of unique items did they carry and how was it distributed? As in, what stayed on the soldier and what stayed with the horse?
The answer to your first question is pretty simple: the paper wadding, rammed home tight on top of the ball and powder, was expected to keep the ball and enough of the charge in place that the weapon would fire after being drawn. Likewise, the frizzen was to shut tight enough over the priming pan that the priming charge would stay in place.
Of course, the longer one rode, the more likely that humidity or jostling would have a deleterious effect on the round in the barrel. Soldiers were expected to clear and clean their firelocks as frequently as possible to enjoy smoother operation.
It's not truly academic, but Don Troiani''s Soldiers of the American Revolution is full of well-researched artistic depictions of 18th century soldiers and displays a dizzying collection of arms and accoutrements from the period, with some descriptions about how soldiers wore and used their equipment.